In the analysis of dynamic systems, we use the term bifurcation to indicate

a dramatic change in the system state, or behavior.

I study milling dynamics, where a bifurcation causes a change from stable to unstable machining conditions. Stable machining gives the desired result, while unstable (or chatter) conditions yield large vibrations, large forces, and poor surface finish. We select machining conditions to avoid chatter. An example of bifurcation behavior in milling is shown in the figure.


I’m not trying to teach you about milling dynamics, though. What occurred to me is that Jesus offers each of us a bifurcation. Through his sacrificial death and resurrection, we now have the gift of grace that allows us to make a dramatic change in our condition. We are able to leap from death to life, from God-separated to God-intimate. Because we have all sinned, we all find ourselves in the God-separated state (chatter). Call on Jesus to forgive your sins, repent of your previous lifestyle, and you’ll be God-intimate (stable)… never again separated from the God who loves you so dearly.


About Tony Schmitz

Tony Schmitz received his BS in Mechanical Engineering from Temple University in 1993, his MS in Mechanical Engineering from the University of Florida in 1996, and his PhD in Mechanical Engineering from the University of Florida in 1999. He is a mechanical engineering professor at the University of North Carolina at Charlotte.
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